Fuzzy continuous function is a section of neoclassical analysis, neoclassical analysis is a synthesis of classical calculus and fuzzy concept. Fuzzy continuous function is better to represent and model reality than continuous function in classical calculus. Therefore, we want to analyze the properties of fuzzy continuity on classical function. The steps are looked for resources that connected with fuzzy continuity concept, and then give description of fuzzy continuity and function as example that form fuzzy continuous function. The next steps are mention and prove theorems that form properties of fuzzy continuity of function.

The discussion of fuzzy continuity based on fuzzy limit concept. There are three approaches to define fuzzy continuity. First, using fuzzy limit of sequence and fuzzy limit of function. Second, deriving and applying discontinuity measures. Third, by-ε,δ construction. At the end research is got the properties of fuzzy continuity of function.

It is recommended for further research to discuss the properties of fuzzy continuity for function and variable.